Asymmetric one-dimensional random walks

For one-dimensional surface diffusion in the presence of fields, movement of particles has to be considered as a random walk in which jumps to the right occur at a rate different from jumps to the left. Moments of the displacement distribution are worked out for such a one-dimensional walk to nearest-neighbor sites as well as by longer jumps to second nearest neighbors. The actual distribution of displacements, and how it changes as the asymmetry of the jump rates changes, is also examined, as this provides important information about the participating jump processes. We show that deriving the third moment gives a clear indication of the asymmetry in the random walk. (C) 2008 American Institute of Physics.